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Let $f:\mathbb{R} \rightarrow \mathbb{R}$ such that $f(x)=x^{5}+x^{3}+1$. Given that $f$ has a root between -1 and 0, how many iterations of interval bisection would be required to obtain the root to an accuracy of $5\times10^{-11}$?

Thanks

Asaf Karagila
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M Smith
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1 Answers1

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On interval $[a,b]$ after $n$ steps you have $|x-x_0|<(b-a)/2^n$, where $x_0$ is root, and $x$ is your result after n iterations. So if $b-a=1$ then your accurcy is given by $1/2^n$, can you do it now?

Z-DNA
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